Utter, utter bobbins.
If someone operating the checkout at Asda gets verbal stick from a succession of customers, will that suddenly make them less competent at carrying out the tasks assigned to a checkout operator? Nope.
What about train drivers? EVERYONE hates train drivers, they get it in the neck all day long. Don't see them accidentally reversing the thing into a tree the next day though.
Estate Agents are massive weapons and therefore must get constant barracking from buyers and sellers alike - how many of them go to work the next day and forget how to take photos of bedrooms because Mr. and Mrs. Simpkins from yesterday called them a lazy git?
Any footballer who says they can't play because they are afraid of the crowd giving them verbal is, in my humble opinion, a very weak-minded person. I'd go so far as to say that they'd struggle in several other lines of work too if they are unable to take criticism.
Part of the job of a top-level footballer is parading your talent in front of your fans - these fans pay a chunk of the wages and have expectations. It's NOT reasonable to demand that the players win every game, because life isn't like that. It IS reasonable however for the fans to expect the players to VISIBLY make the effort, to create the IMPRESSION that they are trying to get a result. Part of that is NOT making stupid decisions every week, or taking HUGELY unnecessary risks. This dovetails nicely into the reasons why it's acceptable for the fans to demand more from the manager too.
Top level football is played in front of crowds of 40,000+ and if you can't handle that, then you can't be a top-level footballer.